Threshold Stochastic Volatility Models with Heavy Tails: A Bayesian Approach

AbstractParticle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

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Use of Stochastic Volatility Models in Epidemiological Data: Application to a Dengue Time Series in São Paulo City, Brazil

Journal of Biostatistics and Epidemiology ◽

10.18502/jbe.v6i1.4755 ◽

2020 ◽

Author(s):

Jorge Alberto Achcar ◽

Ricardo Puziol de Oliveira ◽

Emerson Barili

Keyword(s):

Time Series ◽

Regression Model ◽

Stochastic Volatility ◽

Bayesian Approach ◽

Polynomial Regression ◽

Epidemiological Data ◽

Sao Paulo ◽

São Paulo ◽

Stochastic Volatility Models ◽

Volatility Models

Background: A study on the dengue daily counting in São Paulo city in a fixed period of time is assumed considering a new regression model approch. Methods: Under a Bayesian approach, it is introduced a polynomial linear regression model in presence of some covariates which could affect the counts of dengue in São Paulo city considered in the logarithm scale, combined with existing stochastic volatility models usually assumed in financial data analysis. Markov Chain Monte Carlo methods are used to get the posterior summaries of interest. Results: The new model approach showed some advantages when compared to other existing times series models usually used to model epidemics data. Conclusion: The use of the polynomial regression model combined with existing volatility models under a Bayesian approach showed that it is possible to get very accurate fit for the counting dengue data in São Paulo city where it is possible to jointly model the means and volatilities (variances) of the epidemiological dengue time series.

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Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects

Journal of Risk and Financial Management ◽

10.3390/jrfm14050225 ◽

2021 ◽

Vol 14 (5) ◽

pp. 225

Author(s):

Zhongxian Men ◽

Tony S. Wirjanto ◽

Adam W. Kolkiewicz

Keyword(s):

Stochastic Volatility ◽

Heavy Tails ◽

Foreign Currency ◽

Asset Returns ◽

Stochastic Volatility Model ◽

Stochastic Volatility Models ◽

Asymmetric Effects ◽

Volatility Models ◽

Volatility Model ◽

T Distribution

This paper studies multiscale stochastic volatility models of financial asset returns. It specifies two components in the log-volatility process and allows for leverage/asymmetric effects from both components while return innovation terms follow a heavy/fat tailed Student t distribution. The two components are shown to be important in capturing persistent dependence in return volatility, which is often absent in applications of stochastic volatility models which incorporate leverage/asymmetric effects. The models are applied to asset returns from a foreign currency market and an equity market. The model fits are assessed, and the proposed models are shown to compare favorably to the one-component asymmetric stochastic volatility models with Gaussian and Student t distributed innovation terms.

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